Question

1-2x≤3/x нужно решение с ответом

Answer 1

1-2x≤3/x |*x
-2x≤3-1 |(-2)
x≥-1
ответ: xє(+бескон;-1]

Answer 2

Problem Statement

The equation to solve is: 1 - 2x ≤ 3/x. You need the solution with the answer.

Solution

To solve the equation 1 - 2x ≤ 3/x, we can start by rearranging the terms to get rid of the fraction. Multiplying both sides of the inequality by x will help us achieve this:

x(1 - 2x) ≤ 3

Expanding the left side of the inequality:

x - 2x^2 ≤ 3

Rearranging the terms:

2x^2 - x + 3 ≥ 0

Now, we have a quadratic inequality. To solve it, we can find the roots of the quadratic equation 2x^2 - x + 3 = 0 and analyze the sign of the quadratic expression in different intervals.

The roots of the quadratic equation can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation 2x^2 - x + 3 = 0, the coefficients are a = 2, b = -1, and c = 3. Plugging these values into the quadratic formula, we get:

x = (-(-1) ± √((-1)^2 - 4(2)(3))) / (2(2))

Simplifying:

x = (1 ± √(1 - 24)) / 4

x = (1 ± √(-23)) / 4

Since the discriminant (√(-23)) is negative, the quadratic equation has no real roots. Therefore, the quadratic expression 2x^2 - x + 3 is either always positive or always negative.

To determine the sign of the quadratic expression, we can analyze its concavity. Since the coefficient of the x^2 term is positive, the parabola opens upwards, indicating that the quadratic expression is positive for values of x outside the roots.

Therefore, the solution to the inequality 1 - 2x ≤ 3/x is:

x ∈ (-∞, root1) U (root2, +∞)

Where root1 and root2 are the roots of the quadratic equation 2x^2 - x + 3 = 0.

However, since the quadratic equation has no real roots, the solution to the inequality is:

x ∈ (-∞, +∞)

In other words, any real value of x satisfies the inequality.

Answer

The solution to the inequality 1 - 2x ≤ 3/x is x ∈ (-∞, +∞). This means that any real value of x satisfies the inequality.